Suppose that a comet that was seen in 545 A.D. by Chinese astronomers was spotted again in year 1937. Assume the time between observations is the period of the comet and take its eccentricity as 0.11. What are (a) the semimajor axis of the comet's orbit and (b) its greatest distance from the Sun in terms of the mean orbital radius Rp of Pluto?
I solved the first part by using Kepler's Law of periods and for a semimajor axis which was equal to the radius of the equation.
a=1.89*10^13m
I'm not sure how to solve for Rp, pretty sure it has to deal with eccentricities, but I don't know how to find them.
Scratch that, my numbers are 574 to 1994 and the eccentricity is suppose to be .9932 not .11.
To solve for the greatest distance from the Sun, we can use the concept of eccentricity in the equation. Eccentricity is a measure of how oval-shaped an orbit is, ranging from 0 (perfectly circular) to 1 (highly elongated).
Given that the eccentricity of the comet's orbit is 0.11, we can use this information to find its greatest distance from the Sun in terms of the mean orbital radius of Pluto (Rp).
The key formula you can use here is:
r_max = a * (1 + e)
where:
- r_max represents the greatest distance from the Sun,
- a is the semimajor axis of the comet's orbit, which we already calculated as 1.89 * 10^13 m,
- e is the eccentricity of the orbit, given as 0.11.
Plugging in the values, we have:
r_max = 1.89 * 10^13 * (1 + 0.11)
= 1.89 * 10^13 * 1.11
= 2.1 * 10^13 m
Now, to express this distance in terms of the mean orbital radius of Pluto (Rp), we can divide r_max by Rp:
r_max/Rp = (2.1 * 10^13) / Rp
Unfortunately, without the value of Rp (mean orbital radius of Pluto), we cannot determine the exact numerical value of r_max in terms of Rp. However, you can divide 2.1 * 10^13 by the mean orbital radius of Pluto (Rp) to find the ratio between r_max and Rp.
Please note that Rp can be found through astronomical measurements or through astronomical databases.